Project Overview

To help identify ecosystem and climate influences on American plaice recruitment, distribution, and growth, generalized additive models (GAMs) were used to examine associations between American plaice population dynamics and environmental variables in the Gulf of Maine (GOM) region. This document is meant to serve an a general overview of this analysis. For more details, please refer to Technical Report 16 in Appendix A of the American Plaice Research Track Working Group Report.

Data Sources:

Independent Variable Data:

Bottom Temperature Anomaly:

North Atlantic Oscillation:

Atlantic Multidecadal Oscillation:

Gulf Stream Index:

  • The Gulf Stream Index (GSI) data set was sourced through direct communication with Dr. Zhuomin Chen at Woods Hole Oceanographic Institute where data were derived following the methods of Joyce et al. (2019).

Spawning Stock Biomass (SSB):

  • American plaice SSB data were estimated using spring and fall NEFSC bottom trawl survey numbers at age for American plaice. The aggregate biomass for these indices was calculated for each year (1980-2019) and for each season, in Albatross calibrated units (kg/tow).

Dependent Variable Data:

Recruitment:

Distribution:

Growth:

  • The American plaice condition index data were the same used in the 2022 State of the Ecosystem Report, by NOAA Fisheries. https://apps-nefsc.fisheries.noaa.gov/rcb/publications/soe/SOE-NEFMC_2022-Final.pdf. These data represent the ratio of observed weight:predicted weight from the Fall NEFSC survey and span from 1992-2019.

  • The American plaice weight at age (WAA) anomaly data were calculated from weight at age data used by the American plaice Stock Assessment Research Track working group. These seasonal data are from the NEFSC Survey and span from 1992-2019.

Other Model Information:

GAM Example Formula:

  • gam((WAA_anomaly)~ s(GSI, k=5)+s(AMO, k=5)+s(NAO, k=5)+s(month6_avg_bt,k=5)+s(yearly_bt, k=5), family=tw(),method = “REML”,data=Fall_distribution.df)

  • tested without k (default goes to 10). Can’t run full model at default because there are not enough data to support such a high K.

    • I tested different k values (4,5,6,7,8) and all results either did not have a significant effect on model fit outcomes, or made them worse (increased deviance explained but also increased AIC… signs of the model being overfit)

Response Curves (How to read):

  • GAMs explore the response based in the mean-centered values.

  • As such, the y-axis shows values around zero (the mean).

  • The closer these new (transformed values) are to the zero line, the more it indicates that the smooth curve is basically not explaining the changes in the response.

  • When the curve is above the zero line, it means the original response value was above the average, and vice versa.

  • Unlike linear regression, which uses slope, there is no single quantitative coefficient you can make inference from, so you need to rely on interpreting the partial effects of the smooth visually.

Sources:

In Terms of Recruitment (How to read):

  • Original recruitment data (Age 1) are in units of numbers/tow
  • SSB data are in Albatross units of kg/tow
  • If response curve is above the zero mean line, it means the original response was greater than the average = greater number of recruits/SSB
  • If response curve is below the zero mean line, it means the original response was less than than the average = fewer number of recruits/SSB

In Terms of Distribution (Depth) (How to read):

  • Original data were all negative numbers, meaning an observation of -170m was deeper than a observation of -140m.
  • GAMs used the absolute value of the data, meaning an observation of 170m was deeper than a observation of 140m.
  • If response curve is above the zero mean line, it means the original response was greater than the average = deeper than average
  • If response curve is below the zero mean line, it means the original response was less than than the average = shallower than average

In Terms of Distribution (Latitude) (How to read):

  • Original data are in units of degrees latitude.
  • If response curve is above the zero mean line, it means the original response was greater than the average = more northerly center of gravity
  • If response curve is below the zero mean line, it means the original response was less than than the average = more southerly center of gravity

In Terms of Growth (How to read):

  • Original condition index data represent the ratio of observed somatic weight:predicted somatic weight.

  • If response curve is above the zero mean line, it means the original response was greater than the average = higher condition = fatter fish/length.

  • If response curve is below the zero mean line, it means the original response was less than than the average = lower condition = thinner fish/length.

  • Original weight at age data are in units of mean kg at each age/ year.

  • If response curve is above the zero mean line, it means the original response was greater than the average = greater weight at age.

  • If response curve is below the zero mean line, it means the original response was less than than the average = lower weight at age.

Variables Tested:

  • Gulf Stream Index (6-month and 12-month prior to survey mean)
  • AMO (6-month and 12-month prior to survey mean)
  • NAO (6-month and 12-month prior to survey mean)
    • NAO - lagged additional year (Only used in recruitment models. See Brodziak and O’Brien, 2005)
  • Bottom Temperature Anomaly (6-month and 12-month prior to survey mean)
  • 4-month mean Sea Surface Temperature (SST) (tested only in recruitment models)
    • 4-month SST variables begin in March to align with beginning of peak spawning for plaice.
  • Seasonal spawning stock biomass (Calendar year mean, in Albatross units. Tested only in distribution and growth analyses. In recruitment analysis, SSB, was incorporated into dependent variable (R/SSB))

  • Pearson correlation coefficient tests revealed high dependence between GSI and temperature variables (bottom temperature & SST), as well as between NAO & AMO.

  • 6 month bottom temperature means are September (year-1) - February (year) for spring survey and April (year-1) - September (year) for fall survey.

  • Annual bottom temperature means are March (year-1) - February (year) for spring survey and October (year-1) - September (year) for fall survey.

  • No outliars were removed.

Population Dynamic Examined:

Recruitment:

Raw Data Plots:

Seasonal R/SSB Age 1

Results:

- AMO was significant in both fall and spring models
Model Significant Covariates Full Model Deviance Explained Full Model AIC Reduced Model Deviance Explained Reduced Model AIC
Fall

GSI (1.13%)

AMO - 6-month mean (26.0%)

 53.7% 39.46 33.1% 43.16
Spring AMO -annual mean (36.6%) 63.4% -75.96 36.6% -65.04

Model Diagnostics

Fall GAM Relationship Curves

Spring GAM Relationship Curves

Additional Notes:

- Tweedie GAMs were used and covariates were selected after applying a backwards fitting technique based on covatiate significance (p<0.05) and AIC.

Distribution:

Raw Data Plots:

Seasonal Mean Depth and Latitude of Catches from NEFSC Bottom Trawl Survey

Results:

  • Spring depth model had no significant variables

  • SSB and annual bottom temperature anomaly were significant in both latitude models (spring and fall).

  • Model deviance explained ranged from 55.6-73.9% (See Table Below)

  • Ultimately picked tweedie distribution for each model, though gaussian and gamma distributions were similar in diagnostics. Picked tweedie for combination of best looking residuals and AIC.

  • GAM response curves showed consistency between similar significant variables (Figures 2-4)

Distribution Analysis Model Diagnostic Results
Model Variables Used in Reduced Model (% DE when alone in model) Full Model Deviance Explained (No Duplicates) Full Model AIC Reduced Model Deviance Explained (No duplicates or highly correlated) Reduced Model AIC
Fall Depth

NAO - Annual (16.9%)

6-month Bt Anomaly (7.4%)

SSB (5.99%)

 55.6% 264.2 53.3% 262.43
Spring Depth N/A N/A N/A N/A N/A
Fall Latitude

AMO - 6-Month (3.74%)

Annual Bt Anomaly (24.8%)

SSB (14.1%)

 70.5% -77.39 60.6% -75.87
Spring Latitude

NAO - 6-Month (9.39%)

Annual Bt Anomaly (33.9%)

SSB (14.1%)

 73.9% -101.22 69.5% -101.40

Figure 1: Model fit plots of each season × dependent variable groups. Each Row of plots corresponds to a difference season × dependent variable group where row (1) is fall depth and row (2) is fall latitude, and row (3) is spring latitude.

Figure 2: Fall Mean Depth GAM response curves

Figure 3: Fall Mean Latitude GAM response curves

Figure 4: Spring Mean Latitude GAM response curves

Recommendations:
  • Explore SSB and bottom temperature further for latitudinal and depth changes in distribution.
Additional Notes:
  • Tweedie GAMs were used and covariates were selected after applying a backwards fitting technique based on covariate significance (p<0.05) and AIC.

Growth:

Raw Data Plots:

Condition Index Data

Figure 1: Fall Mean Condition Indices

Weight at Age Anomaly Data

Figure 2: Fall WAA Anomalies for Plaice Ages 1-5

Figure 3: Fall WAA Anomalies for Plaice Ages 6-11+

Figure 4: Spring WAA Anomalies for Plaice Ages 1-5

Figure 5: Spring WAA Anomalies for Plaice Ages 6-11+

Results:

Condition Index Test
Model Significant Covariates Full Model Deviance Explained Full Model AIC Reduced Model Deviance Explained Reduced Model AIC
Fall

6-Month AMO (10.2%)

Annual Bottom Temperature Anomaly (12.1%)

SSB (25.5%)

 58.3% -107.28 57.5% -111.255

Figure 6: Fall Mean Condition Model Diagnostics

Figure 7: Fall Mean Condition GAM Response Curves

Weight at Age Test:

  • Fall age 8 and Spring age 1 had no significant variables

  • GSI was significant in younger age classes (2-4 for Fall and ages 2-6 for spring)

  • AMO was significant in every year class (except age 1 (fall and spring), and in age 8 (fall specifically))

  • SSB was significant for ages 3-5 in Fall and 5-6 in Spring

  • Bottom temperature anomalies were significant in more year class extremes (Age 1 & 9 in fall, 10 & 11 in spring)

  • GAM response curves showed consistency between similar significant variables (Figures 11-14)

Figure 8: Visualizing Significant Variables by Year Class

Table 1: Fall Model Results

Table 2: Spring Model Results

Figure 9: Model diagnostic fit plots for fall

Figure 10: Model diagnostic fit plots for spring

Figure 11: Fall Ages 1-5 WAA Anomlay GAM response curves

Figure 12: Fall Ages 5-11+ WAA Anomlay GAM response curves

Figure 13: Spring Ages 2-4 WAA Anomlay GAM response curves

Figure 14: Fall Ages 5-11+ WAA Anomlay GAM response curves

Recommendations:

  • Explore AMO and GSI, consider SSB and Bottom Temperature Anomaly, depending on age class of interest.

Additional Notes:

  • GAM response curve plots are difficult to read, but are meant to show consistency of trends/curve shapes

  • Gaussian GAMs were used and covariates were selected after applying a backwards fitting technique based on covariate significance (p<0.05) and AIC.